Why fractions are hard
What’s So Hard About Fractions?
Fractions as we know them today, the symbols and the algorithms for performing operations, have developed over thousands of years, beginning with ancient Egyptians. Through research of the origins, the development of fractions to appearing symbolically as we know them today, and of the developments of how we operate with them today and then connecting that knowledge with the observations of contemporary math education experts and personal interviews and observation of fifth grade students learning fractions it has become evident that the development of fractions took thousands of year and suffered many complications. It is most evident that knowledge of that which birthed and stunted the development of fractions is similar to what stunts instruction and confuses many students in their understanding of fractions and their algorithms as we know them today.
Before delving into what is so hard about fractions it seems more appropriate to being to answer the following two questions; Why were fractions invented and what purpose do they serve? Ancient Egyptians, as long ago as 2000BC (citation), knew that fraction were essential when needing more precise or even exact measurements, or measurements that fell between two whole numbers, without switching units. Fractions therefore serve the purpose of measurement and for finding a value betweens two whole numbers, for more precise numerical value. That is, it has been deducted by historians that fractions were first deemed necessary in ancient civilization because of their need in precision of measurement, and not in terms of division. It wasn’t until the eleven century when the definition of fractions was determined to be the division between two numbers ( PDF citation). This is in contrast the way fractions are introduced in schools today. To solve problems associated with numbers falling between two numbers, Ancient Egyptians developed unit fractions. They were breaking a whole
Fractions as we know them today, the symbols and the algorithms for performing operations, have developed over thousands of years, beginning with ancient Egyptians. Through research of the origins, the development of fractions to appearing symbolically as we know them today, and of the developments of how we operate with them today and then connecting that knowledge with the observations of contemporary math education experts and personal interviews and observation of fifth grade students learning fractions it has become evident that the development of fractions took thousands of year and suffered many complications. It is most evident that knowledge of that which birthed and stunted the development of fractions is similar to what stunts instruction and confuses many students in their understanding of fractions and their algorithms as we know them today.
Before delving into what is so hard about fractions it seems more appropriate to being to answer the following two questions; Why were fractions invented and what purpose do they serve? Ancient Egyptians, as long ago as 2000BC (citation), knew that fraction were essential when needing more precise or even exact measurements, or measurements that fell between two whole numbers, without switching units. Fractions therefore serve the purpose of measurement and for finding a value betweens two whole numbers, for more precise numerical value. That is, it has been deducted by historians that fractions were first deemed necessary in ancient civilization because of their need in precision of measurement, and not in terms of division. It wasn’t until the eleven century when the definition of fractions was determined to be the division between two numbers ( PDF citation). This is in contrast the way fractions are introduced in schools today. To solve problems associated with numbers falling between two numbers, Ancient Egyptians developed unit fractions. They were breaking a whole
Bibliography: Mack, N. K. (1990). Learning fractions with understanding. Building on informal knowledge. Journal for Research in Mathematics Education, 21(1), 16--32. Erlwanger, S. H. (1973). Benny 's conception of rules and answers in IPI mathematics. Journal of Children 's Mathematical Behavior, 1(2), 7-26. Ifrah, G., & Bellos, D. (1998). The universal history of numbers: From prehistory to the invention of the computer. London: The Harvill Press. Clarke, Doug M., Anne Mitchell, and Ann Roche. "10 Practical Tips for Making Fractions Come Alive and Make Sense." Mathematics Teaching in the Middle School. Volume 13.Issue 7 (2008): 373 – 380. Print.